It is over 45 years since it was discovered that cosmic rays exist with energies greater than 1 Joule. We now know the energy spectrum and arrival-direction distribution of these very energetic particles in considerable detail up to energies some 16 times greater (~1020 eV) and are beginning to get insights as to how their mean mass changes with energy. I will describe the studies of these topics, largely made using the Pierre Auger Observatory, and will say something about the astrophysical implications of the measurements.
We are hampered in deducing more about the mass of the highest-energy particles by our lack of knowledge of hadronic interactions, particularly pion interactions, at centre-of-mass energies well beyond those reached at the LHC. As our contribution to elucidating these difficulties, we have measured the proton-air cross-section at a centre-of-mass energy of 57 TeV and have established that showers contain more muons than predicted by extrapolation of models rooted in LHC measurements.